A fully coupled numerical method for coaxial borehole heat exchangers using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.svg"> <mml:msub> <mml:mstyle displaystyle="false" scriptlevel="0"> <mml:mtext>CO</mml:mtext> </mml:mstyle

We present a new fully coupled and implicit numerical method for the solution of the pressure and the temperature of a coaxial borehole heat exchanger (CBHE) using compressible working fluids such as supercritical ( ). The objective is to present and test a robust simulation approach with good convergence properties for the design and operation of CBHE utilizing compressible fluids. The model is based on cylindrical symmetry, and the transient heat conduction in the rock is treated with the finite element method (FEM), while conservation of mass, momentum, and energy in the well is treated by a finite difference method (FDM). The new feature of the model is that all unknowns have a corresponding node in a regular FE grid. Using the nodes in the FE grid for both the FEM in the rock and the FDM in the well simplifies the integration of the two different numerical methods as well as the allocation of the system matrix. The numerical approach is benchmarked against a 1-D analytical solution for the case of a constant mass flow rate of an incompressible fluid, and a 1-D numerical implementation for . The benchmarking is considered excellent based on the misfit measured as root mean square (RMS) error. The model is used to compare heat production using liquid/supercritical and under the same operating conditions over a range of mass flow rates. The comparison shows that gives a higher heat production than does for all flow rates. gives a higher output temperature for low flow rates due to its low compressibility, while gives a higher output temperature for the high-end flow rates because of its lower heat capacity and viscosity. • A fully coupled and implicit scheme for pressure and temperature of a CBHE. • Shared FE grid between rock (FEM) and well (FDM). • Excellent convergence properties. • Comparison of and as working fluids.